BRST quantization and cohomology
imported>Pythagoras0님의 2012년 10월 28일 (일) 15:22 판 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로)
introduction
- gauge theory = principal G-bundle
- we require a quantization of gauge theory
- BRST quantization is one way to quantize the theory and is a part of path integral
- gauge theory allows 'local symmetry' which should be ignored to be physical
- this ignoring process leads to the cohomoloy theory.
- gauge theory allows 'local symmetry' which should be ignored to be physical
- BRST = quantization procedure of a classical system with constraints by introducing odd variables (“ghosts”)
- re-packaging of Faddeev-Popov quantization
- the conditions D = 26 and α0 = 1 for the space-time dimension D and the zero-intercept α0 of leading trajectory are required by the nilpotency QB2 = 0 of the BRS charge
gauge fixing==
ghost variables==
Faddeev-Ghost determinant==
- Faddeev-Popov ghosts, Hitoshi Murayama
path integral and ghost sector==
- \(Z = \int\!\mathcal{D}X\,\mathcal{D}c \mathcal{D}b \mathcal{D}\bar{c} \mathcal{D}\bar{b} \,e^{-\int\left(\partial X \partial \bar{X} -b_{zz}\partial_{\bar{z}}c^{z}+b_{\bar{z}\bar{z}}\partial_{z}c^{\bar{z}}\right)}\)
- \(e^{S_1(X)+S_2(b,c,\bar{b},\bar{c},\cdots,X)\)
- DX : matter and Db : ghost Dc : antighost
- bc system of \epsilon=+1 (in Faddeev–Popov ghost fields)
- \lambda=2
- c_{b,c}=-26
- [c]=-1,[b]=2
- global issues
- discrepancies in conformal gauge
- moduli spaces
- CKV
- path integral and moduli space of Riemann surfaces
- discrepancies in conformal gauge
- moduli spaces
- CKV